Evaluate the change in redshift over 10 years

[HawkEye5220]

Homework Statement

I am given a model where for an accelerating universe the redshift changes according to the following equations (given in part b). For this model and assuming that H₀=70km/s/Mpc, evaluate the change in redshift over 10 years, for a source at z=1 and the change in recession velocity

Homework Equations

rate of change is $\frac{dz}{dt}$=H₀(1+z)-H(z) where H(z) is the Hubble parameter
In this case I am considering a κ=0 universe with no cosmological constant, so H(z)=H₀(1+z)^3/2

The Attempt at a Solution

I know that the long way would be to take the integral of the $\frac{dz}{dt}$ formula from z=1 to z' over the entire time period. What I am wondering is, because of how minute the change would probably be is it acceptable to approximate this as:
Δz≈t1H₀(1+z-((1+z)^3/2)) where t1=10 years?

 

[HawkEye5220]

I am asking because when I calculate this I get a negative number for the change in z. Wouldn't this be a blueshift?